TY - GEN
T1 - Low-Rank Parity-Check Codes over the Ring of Integers Modulo a Prime Power
AU - Renner, Julian
AU - Puchinger, Sven
AU - Wachter-Zeh, Antonia
AU - Hollanti, Camilla
AU - Freij-Hollanti, Ragnar
N1 - Publisher Copyright:
© 2020 IEEE.
PY - 2020/6
Y1 - 2020/6
N2 - We define and analyze low-rank parity-check (LRPC) codes over extension rings of the finite chain ring {{\mathbb{Z}}-{{p^r}}}, where p is a prime and r is a positive integer. LRPC codes have originally been proposed by Gaborit et al. (2013) over finite fields for cryptographic applications. The adaption to finite rings is inspired by a recent paper by Kamche et al. (2019), which constructed Gabidulin codes over finite principle ideal rings with applications to space-time codes and network coding. We give a decoding algorithm based on simple linear-algebraic operations. Further, we derive an upper bound on the failure probability of the decoder. The upper bound is valid for errors whose rank is equal to the free rank.
AB - We define and analyze low-rank parity-check (LRPC) codes over extension rings of the finite chain ring {{\mathbb{Z}}-{{p^r}}}, where p is a prime and r is a positive integer. LRPC codes have originally been proposed by Gaborit et al. (2013) over finite fields for cryptographic applications. The adaption to finite rings is inspired by a recent paper by Kamche et al. (2019), which constructed Gabidulin codes over finite principle ideal rings with applications to space-time codes and network coding. We give a decoding algorithm based on simple linear-algebraic operations. Further, we derive an upper bound on the failure probability of the decoder. The upper bound is valid for errors whose rank is equal to the free rank.
UR - http://www.scopus.com/inward/record.url?scp=85090420499&partnerID=8YFLogxK
U2 - 10.1109/ISIT44484.2020.9174384
DO - 10.1109/ISIT44484.2020.9174384
M3 - Conference contribution
AN - SCOPUS:85090420499
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 19
EP - 24
BT - 2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2020 IEEE International Symposium on Information Theory, ISIT 2020
Y2 - 21 July 2020 through 26 July 2020
ER -